The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A176999 An encoding of the Collatz iteration of n. 3
 1, 1111010, 11, 11110, 11110101, 1111011101101010, 111, 1111011101101010110, 111101, 11110111011010, 111101011, 111101110, 11110111011010101, 11110111110101010, 1111, 111101110110, 11110111011010101101, 11110111011010111010, 1111011, 1111110, 111101110110101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Working from right to left, the sequence of 0's and 1's in a(n) encode, respectively, the sequence of 3x+1 and x/2 steps in the Collatz iteration of n. This is reverse one's complement of Garner's parity vector. Criswell mentions this encoding. The length of a(n) is A006577(n). The number of 1's in a(n) is A006666(n). The number of 0's in a(n) is A006667(n). The number of terms having length k is A005186(k). LINKS T. D. Noe, Table of n, a(n) for n = 2..10000 Evans A. Criswell, The Collatz Problem (3x+1) Lynn E. Garner, On heights in the Collatz 3n+1 problem, Discrete Math, 55 (1985), 57-64. EXAMPLE a(5)=11110 because the Collatz iteration for 5 is a 3x+1 step (0) followed by 4 x/2 steps (four 1's). MATHEMATICA encode[n_]:=Module[{m=n, p, lst={}}, While[m>1, p=Mod[m, 2]; AppendTo[lst, 1-p]; If[p==0, m=m/2, m=3m+1]]; FromDigits[Reverse[lst]]]; Table[encode[n], {n, 2, 26}] CROSSREFS Sequence in context: A235221 A060087 A229783 * A035613 A038449 A262498 Adjacent sequences:  A176996 A176997 A176998 * A177000 A177001 A177002 KEYWORD nonn AUTHOR T. D. Noe, Apr 30 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 22 21:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)